Following is the unofficial transcript of a CNBC EXCLUSIVE interview with CNBC's Steve Liesman and United States Secretary of the Treasury Jacob Lew. Following is a link to video: http://video.cnbc.com/gallery/?video=3000416564. The full interview will be available on CNBC.com.

All references must be sourced to CNBC.

STEVE LIESMAN: Mr. Secretary, thanks for joining us.

JACK LEW: Great to be with you, Steve.

STEVE LIESMAN: Let's talk about recent market volatility. You've had massive swings in the markets. Is that a cause of concern to you, either systemic risk or some concern that perhaps there's some underlying problems in the U.S. economy?

JACK LEW: You know Steve, from the perspective of the U.S. economy, I think while we've seen substantial volatility in markets, we've seen continuing signs of strength in the U.S. economy. Even in these last few days we've seen the consumer activity remain strong. Auto sales were very strong. So we've had a consistent and quite stable series of indicators that the U.S. economy remains strong. We are keeping a careful eye on market volatility. We are looking at what, if any, risks there are. And so far have not seen the kinds of stresses in financial institutions that would cause us to have any immediate concerns. But we're obviously always watching as there's developments.

STEVE LIESMAN: It was a Monday about a week ago that the market opened up down 1,000 points. Tell us where the Treasury Secretary was, what you were doing and most importantly what you were thinking when the market falls 1,000 points.

JACK LEW: You know, Steve, I keep my eye on the market, but I try to not respond immediately and form judgments based on minute-to-minute or day-to-day market moves. What I tend to do is to reach out to my colleagues, other finance ministers, to central bankers. I reach out to senior leaders in the in the financial world to get their views, other experts. And you know, there was a pretty strong sense at that moment that it was a response to some specific concerns, particularly concerns about China. And you know, I think the day-to-day market moves are less what I focus on than what are the core economic directions the different parts of the U.S. economy are taking. And as I said, I think those are remaining very stable.

STEVE LIESMAN: I want to talk about China just for a second, but I want to get back to this 1,000 point – these massive swings we've had. Do you have concerns about high frequency trading – computer trading, is it something that we need to do more to perhaps because it creates such systemic risk?

JACK LEW: You know, it is obviously something we need to continue to look at and ask exactly the question that you've asked. When you see the market open and close with dramatic movements and it raises questions as to whether there are things in the architecture of the markets, the structure of the markets, that are contributing to some of the moves. I don't have a clear answer for you. I don't think, frankly, anyone has a very clear answer. Except there is a set of questions which we've raised already about some other events in the market as to whether there's something-- about the evolving structure of the market that requires more attention. I think we have to do a lot more thinking and study on this before we form a view.

STEVE LIESMAN: There's more attention and even perhaps more regulation, an idea that maybe there shouldn't be so much – such an ability of computers to go in and control the trading?

JACK LEW: I think it's premature and you know, when I've looked at this over the course of the last three years several times, the questions of high frequency trading, it seems to me that, you know, it falls into several different baskets of concerns. The two that I think we have to keep our eye on are is there something that the plumbing of the system that's undermined by high frequency trading or is their unfair advantage that's gained because of the way it's structured. You know, I don't think it's a great idea for us to pick and choose what forms of investment and market practices are the way of the future. I think government's trying to think that through for markets can get you to a bad place. But I do think we have a responsibility to ask questions about whether the markets are being stressed in ways that create risk or create some kind of unfair advantage or disadvantage. I think that the events you know, this last week, you know, kind of raise questions about how do the normal mechanisms in the market stop trading events, pauses, interact with high frequency trading and have people thought through all of the ramifications. As I say, I can't tell you that I have an answer to that. Many of these issues fall well within the jurisdiction of the Securities and Exchange Commission. But I think they're important questions.

STEVE LIESMAN: Let me pivot to China then and talk about how much concern or ask you how much concern you have over Chinese economic weakness, especially when it comes to U.S. economic growth.

JACK LEW: You know, I think you have to start by where the U.S. economy is. And you know, I'm happy to say the U.S. economy is being looked at as being one of the bright spots in the global economy right now because we've taken the steps we need to, to come out of a deep recession. We've been growing you know, for a good and sustained period of time. We're seeing good sustained job growth. And we're seeing increasingly strong consumer demand. So I think we started out with – and we always want to do better. So I'm not complacent. We want to do even better than we're doing. But we start out by global standards with a strong U.S. economy. I think China for some time has been slowing down. You know, they had a double digit growth rate that was fueled by, you know heavy growth of industry. And they have for several years now been in a transitional phase. The question is are they managing that transition in an effective and orderly way. I think that there's no question in my mind that the message we have given to our friends in China is one that at a policy level they embrace, which is that there needs to be a set of reforms put in place where the economy becomes much more market oriented, where consumer demand grows and there's a shift from a heavy, heavy emphasis on industrial spending to more and more consumer driven spending. And I think that what they're experiencing now is the challenge of managing that transition in an orderly way. I think the really important question for the medium and the long term is do they have the ability to stick to the reform plan that they've mapped out. Because what they have mapped out is a set of steps that reflects the kinds of concerns that we've raised and the kinds of commitments they've made to us over the years. And I think that what we've seen over the last few weeks are some moments of policy action that have caused people to question whether that is sustained. You know, we'll have opportunities to meet directly. I've spoken with the Chinese economic leaders over the last couple of weeks. I'm going to be seeing some of them at the G20 meeting in just a few days. But I think it's actually broader than China in the sense that there's a question here about demand, worldwide demand being a bit soft. And while U.S. demand is doing well, it's not strong enough to pull the whole global economy forward. And that's why one of the issues at the G20 that we'll be dealing with is actions that can be taken in China to reform and move towards consumer demand but in other parts of the world to have more emphasis on growth and demand.

STEVE LIESMAN: I do want to talk about the G20 in just a second. But I just want to get back to China, a couple other questions there. If there's further devaluation of the yuan, will that give you concern that China's trying to depreciate its way out of its problems and do so in a way at the expense of the United States?

JACK LEW: Look, I think that we have been very clear for a very long time with China that how they manage their exchange rate is a matter of great concern to us and that they need to be willing to let market forces drive the value up, not just drive it down. And that's a message I've delivered very clearly. You know, I think at a moment when their economy is weakening as opposed to strengthening, you know, it's easy to say the pressures are to go down, not up. But this is not a new conversation. This is a conversation that's been going on for some time. So we need to see a serious commitment to the kind of reform agenda that makes it clear that over time, you know, their currency will go up as their economy is strengthening. And they need to be committed to the kinds of policies that will contribute to stronger economic growth. So there's a very important area of engagement, but it's actually something where it's important not just for the United States. It's important for China. China needs to have that kind of strong, stable growth. The global economy needs for China to have that strong, stable growth. And I don't think they can get it if they back away from the reform path that they've committed to. They've made progress over the years that I've been engaged with them on this exchange rate issue. And I think, you know, the pressure is going to be are they willing to take the market forces and let it drive the R&B up as well as down.

STEVE LIESMAN: Republican presidential contender Donald Trump says what's going on with China's economic policy has come out to the greatest theft in history. Says the Chinese are stealing American jobs, stealing American money. Do you have concern, first of all, that that kind of populist talk is playing in the election right now as well as some concerns that Chinese – how do you respond to Donald Trump?

JACK LEW: I think that I don't need to look to the political statements to focus on the importance of the U.S./China economic relationship. It is an enormously important relationship. It's one where China needs to understand quite clearly that we expect for them to behave in a way that's consistent with agreements that they have made, where we expect them to behave in a way that meets a level of transparency where it's credible that they're moving to keep commitments that they've made. And they have to understand, and I make this point to them quite clearly, that there's an economic and a political reality to things like exchange rates. And they need to understand that they signal their intentions by the actions they take and the way they announce them. And they have to be very clear that they're continuing to move in a positive direction. And we're going to hold them accountable to do that. I think that the you know, the fundamental concern that-we all should have is what is the core condition and health of the Chinese economy. And are they taking the steps they need to grow it. And within that, are they prepared to live with a level playing field and play by the kinds of rules where there can be fair competition. Those are the kinds of things they've committed to us. Those are the kinds of things we're going to hold them accountable to.

STEVE LIESMAN: But you would reject the notion of calling this theft, these policies, this stealing American jobs and American money?

JACK LEW: I'm happy to talk about the U.S./China relationship. I'm going to stay clear of the political campaign. One of the great things of being Treasury Secretary is you don't get involved in politics.

STEVE LIESMAN: When you travel to Turkey, could you talk about the message you have for the G20 countries, especially when it comes to currencies? A lot of currencies have depreciated fairly strongly against the U.S. dollar. Is there concern on your part that some of this has gone too far?

JACK LEW: I think that I've said on a number of occasions, I think you and I have talked about it's not a great thing if you get into a situation where there's any even appearance of competitive devaluation. That's not good for our relationships with other countries, it's not good for the global economy. I think what you have going on right now is a time when you have economic forces that are operating in different directions in different countries. And you have second order effects that are very real. So the U.S. economy is stronger than many other economies in the world. That creates a certain stress there. You have quite a number of countries, particularly emerging market countries, that are very closely connected to China as suppliers of commodities. And they're feeling economic pressures because of the slowing the rate of growth in China. So I think this is a complicated time economically but that we all have to avoid and I think it is something we will discuss at the G20 is any temptation to slip into what might look like competitive devaluation. It's both unfair and it ultimately leads to a worse global economy.

STEVE LIESMAN: Mr. Secretary, there is one question on China that I forgot to ask, which is China recently arrested a journalist for spreading a report essentially about whether or not the government would intervene. Apparently there were some 200 other people arrested. Is there a role for treasury in terms of the way it promotes economic reform in China to deal with, to address that issue with Chinese authorities?

JACK LEW: Well obviously transparency means that you can both see and talk about what's happening in the economy and in the government's economic policy. That is an important principle. It's something that you know, I believe is part of being one of the leading economies in the world. You have to be willing to be more transparent. I think rule of law is a second principle that's critically important to having the kind of economy that we have here in the United States and that China is trying to build. So I think, you know, both transparency and rule of law have to be core principles.

STEVE LIESMAN: Is it something though you would address specifically with Chinese authorities?

JACK LEW: Well, you know, I'd have to know more about the circumstances to answer that, Steve. But I have raised questions of transparency and rule of law and will continue to.

STEVE LIESMAN: Just a couple other sort of trips around the world here when it comes to the question of Greece do you have concern that the International Monetary Fund ultimately may not be involved in some package of loans to Greece because of concerns over debt restructuring?

JACK LEW: Look, I think that it's a very important thing that Europe has reached a point of agreement on an approach forward on Greece. I've put an enormous amount of my time into helping to bring parties together and to promote a sensible discussion where there's real serious reforms in Greece and a willingness on the part of European countries to continue to provide the necessary support. I also think the IMF has played a critical role both in terms of validating the steps taken, but also bringing the issue of debt restructuring squarely into focus. It's an issue that I have spoken to on quite a number of occasions and made clear we agree and believe that there's a need for debt restructuring. To deal with, you know, a long term path ahead. I think what you've had in this last negotiation was an agreement both on a program and to have a discussion in the fall on the question of debt restructuring. I think that's an important discussion. I certainly hope that the parties come to it with the same pragmatic approach that we saw in the last round of negotiations and not what we saw in some earlier rounds of negotiations.

STEVE LIESMAN: But are you confident the IMF will be involved in helping with the next backed financial –

JACK LEW: I think the IMF has said quite clearly that the debt sustainability review is one that is an essential part of their decision to participate. Debt restructuring fits into that. And I'm certainly hopeful that there will be a debt restructuring agreement that gives the IMF the ability to have a positive conclusion to the debt sustainability review. I can't speak for the IMF. I think the IMF has played a very important role in this. But I also think that the issues they have raised about debt sustainability is very real. And it's one that there has been an agreement at a leader's level to, you know, have, you know, a serious engagement on. Obviously there's going to be a little bit of a time out now as there's a Greek election. But it'll be October before we blink.

STEVE LIESMAN: Today we learned that the President seems to have enough votes in order to sustain a veto of any legislation that would block-- the deal with Iran. Is there a day that's fairly soon where American companies will be doing business in Iran? And when is that day?

JACK LEW: You know, Steve, it's very important that we have now established that we have sufficient votes so that we can say this agreement will be implemented. We're not done working on the agreement. It's a good agreement that would stop Iran from having a nuclear weapon and gives us tools to see what they're doing and hold them accountable and put sanctions back in place if we need to. And I think that's why we've gotten to 34 votes in the Senate. We're still working for every vote that's out there the stronger the vote is, the better it is for our proceeding forward. And we don't consider it a job done, though today was an important threshold. An important message that I've given both to businesses in the United States and overseas and to financial leaders, finance ministers around the world, is none of the sanctions that will be lifted when Iran complies are lifted yet. They're all in place until Iran completes all of the steps that it has to take. So there should be no misunderstanding that because there's a vote in Congress or because we've passed some initial date that the sanctions are gone. We are going to continue implementing the sanctions until Iran complies. And I might note that after Iran complies with a nuclear agreement, we'll continue to have sanctions in place that are to address terrorism and global destabilization. I think the challenge that we have is to make that clear so that no firm is out there doing business and saying, "Well, we didn't know. We thought that because there was a vote, you know, the coast was clear." Iran will not be free from these sanctions until they comply. And we don't know when that will be exactly.

STEVE LIESMAN: Are the Europeans out there already jumping the gun? Is there some concern about that?

JACK LEW: I watch this pretty closely and I see trips to Iran by European businesses and some ministers. And to my knowledge all they've been having is kind of conversations, opening conversations. I have made quite clear to them that any company that does business in the United States is subject to U.S. law. And we are going to be continuing to proceed with the enforcement of sanctions until we get to the point that Iran has complied. So I actually don't think that we're in a place where business is being transacted in real time. You know, there may be some desire on the part of some to be the first ones in the door having conversations. That's their judgment. But to the extent that they think that the sanctions are lifted, they need to be aware that it requires Iran taking all of the steps to shut down all four pathways to a nuclear weapon before those sanctions are lifted. And then they still have to be cognizant of the remaining sanctions for other purposes.

STEVE LIESMAN: You were at the State Department when Hillary Clinton was Treasury Secretary. Were you aware she was using a private server? Did you object at the time?

JACK LEW: You know, Steve, my contact with Secretary Clinton was usually in person or on the phone. I did have email contact with her. I mostly paid attention to the content of the emails and didn't actually pay as much attention to what the email address was. My focus was always on the substance of what we were doing. And as I've now seen you know, the kind of things that come out, you know, my emails were always appropriate.

STEVE LIESMAN: Jack, we did Iran, China, Greece, is there a part of the world I didn't ask about that I should be asking about?

JACK LEW: Well there's certainly other parts of the world, I mean—

STEVE LIESMAN: There's Russia we didn't talk about.

JACK LEW: There is Russia we didn't talk about, we didn't talk about other parts of Asia. You know I think that it'll be an important time for getting together at the G20 meeting to hear how other countries are seeing both the volatile markets and the, you know, prospect for economic growth domestically and in other countries. Because a lot of what's going on right now is I think trying to understand what will be the effect on my country by developments in other countries. And you know, it's the global connections, you know, flow through trade and they flow through, you know, other institutions as well. So I think that it'll be an important set of conversations to see you know, how much dependence there is on the United States. I think that people will be looking to the United States as a kind of beacon of, you know, economic energy. And we're going to bring the message that you need to take the actions in your economies to boost demand and grow at home and boost the global economy so that we can all be doing better.

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